f(z)=z
import domcol;
size(15cm);
pair f(pair z) { return z; }
pair a = (-5, -5), b = (5, 5);
real c = 0;
pair[][] z = map_rect(f, a, b);
int[] H = image(z, a, b, c, reverse=true);
xaxis(Bottom, a.x, b.x, RightTicks(N=2, n=5));
yaxis(Left, a.y, b.y, LeftTicks(N=2, n=5));
pair pa = (b.x + 0.5, a.y);
pair pb = (b.x + 2, b.y);
real[] rs = rtpalette(c, H, pa, pb);
isomodulus(z, a, b, rs);
isophase(z, a, b);
draw(box(a, b));
f:(xy)↦(acbd)(xy)=A(xy)f(z)=f(x+iy)=2(a+d)+i(c−b)z+2(a−d)+i(c+b)zA=(11−13)f(z)=(2+i)z+z
import domcol;
size(15cm);
pair f(pair z) { return (0, 0, 1, -1, 1, 3) * z; }
pair a = (-5, -5), b = (5, 5);
real c = 0;
pair[][] z = map_rect(f, a, b);
int[] H = image(z, a, b, c, reverse=true);
xaxis(Bottom, a.x, b.x, RightTicks(N=2, n=5));
yaxis(Left, a.y, b.y, LeftTicks(N=2, n=5));
pair pa = (b.x + 0.5, a.y);
pair pb = (b.x + 2, b.y);
real[] rs = rtpalette(c, H, pa, pb);
isomodulus(z, a, b, rs);
isophase(z, a, b);
draw(box(a, b));
f(z)=z2+2+2i(z2−1)(z−2−i)2
import domcol;
size(15cm);
pair f(pair z) { return (z * z - 1) * (z - (2, 1))**2 / (z * z + (2, 2)); }
pair a = (-5, -5), b = (5, 5);
real c = 0;
pair[][] z = map_rect(f, a, b);
int[] H = image(z, a, b, c, reverse=true);
xaxis(Bottom, a.x, b.x, RightTicks(N=2, n=5));
yaxis(Left, a.y, b.y, LeftTicks(N=2, n=5));
pair pa = (b.x + 0.5, a.y);
pair pb = (b.x + 2, b.y);
real[] rs = {1, 2, 4, 8, 16, 32};
rtpalette(c, H, pa, pb, rs);
isomodulus(z, a, b, rs);
isophase(z, a, b);
draw(box(a, b));
f(z)=ez
import domcol;
size(15cm);
pair f(pair z) { return exp(z); }
pair a = (-5, -5), b = (5, 5);
real c = 0;
pair[][] z = map_rect(f, a, b);
int[] H = image(z, a, b, c, reverse=true);
xaxis(Bottom, a.x, b.x, RightTicks(N=2, n=5));
yaxis(Left, a.y, b.y, LeftTicks(N=2, n=5));
pair pa = (b.x + 0.5, a.y);
pair pb = (b.x + 2, b.y);
real[] rs = rtpalette(c, H, pa, pb);
isomodulus(z, a, b, rs);
isophase(z, a, b);
draw(box(a, b));
f(z)=cos(z)=2eiz+e−iz
import domcol;
size(15cm);
pair f(pair z) { return cos(z); }
pair a = (-5, -5), b = (5, 5);
real c = 0;
pair[][] z = map_rect(f, a, b);
int[] H = image(z, a, b, c, reverse=true);
xaxis(Bottom, a.x, b.x, RightTicks(N=2, n=5));
yaxis(Left, a.y, b.y, LeftTicks(N=2, n=5));
pair pa = (b.x + 0.5, a.y);
pair pb = (b.x + 2, b.y);
real[] rs = {0.707, 1, 2, 5, 10, 20};
rtpalette(c, H, pa, pb, rs);
isomodulus(z, a, b, rs);
isophase(z, a, b);
draw(box(a, b));
f(z)=sin(z)=2ieiz−e−iz
import domcol;
size(15cm);
pair f(pair z) { return sin(z); }
pair a = (-5, -5), b = (5, 5);
real c = 0;
pair[][] z = map_rect(f, a, b);
int[] H = image(z, a, b, c, reverse=true);
xaxis(Bottom, a.x, b.x, RightTicks(N=2, n=5));
yaxis(Left, a.y, b.y, LeftTicks(N=2, n=5));
pair pa = (b.x + 0.5, a.y);
pair pb = (b.x + 2, b.y);
real[] rs = {0.707, 1, 2, 5, 10, 20};
rtpalette(c, H, pa, pb, rs);
isomodulus(z, a, b, rs);
isophase(z, a, b);
draw(box(a, b));
f(z)=cosh(z)=2ez+e−z
import domcol;
size(15cm);
pair f(pair z) { return (exp(z) + exp(-z)) / 2; }
pair a = (-5, -5), b = (5, 5);
real c = 0;
pair[][] z = map_rect(f, a, b);
int[] H = image(z, a, b, c, reverse=true);
xaxis(Bottom, a.x, b.x, RightTicks(N=2, n=5));
yaxis(Left, a.y, b.y, LeftTicks(N=2, n=5));
pair pa = (b.x + 0.5, a.y);
pair pb = (b.x + 2, b.y);
real[] rs = {0.707, 1, 2, 5, 10, 20};
rtpalette(c, H, pa, pb, rs);
isomodulus(z, a, b, rs);
isophase(z, a, b);
draw(box(a, b));
f(z)=sinh(z)=2ez−e−z
import domcol;
size(15cm);
pair f(pair z) { return (exp(z) - exp(-z)) / 2; }
pair a = (-5, -5), b = (5, 5);
real c = 0;
pair[][] z = map_rect(f, a, b);
int[] H = image(z, a, b, c, reverse=true);
xaxis(Bottom, a.x, b.x, RightTicks(N=2, n=5));
yaxis(Left, a.y, b.y, LeftTicks(N=2, n=5));
pair pa = (b.x + 0.5, a.y);
pair pb = (b.x + 2, b.y);
real[] rs = {0.707, 1, 2, 5, 10, 20};
rtpalette(c, H, pa, pb, rs);
isomodulus(z, a, b, rs);
isophase(z, a, b);
draw(box(a, b));
f(z)=logz
import domcol;
size(15cm);
pair f(pair z) { return log(z); }
pair a = (-5, -5), b = (5, 5);
real c = 0;
pair[][] z = map_rect(f, a, b);
int[] H = image(z, a, b, c, reverse=true);
xaxis(Bottom, a.x, b.x, RightTicks(N=2, n=5));
yaxis(Left, a.y, b.y, LeftTicks(N=2, n=5));
pair pa = (b.x + 0.5, a.y);
pair pb = (b.x + 2, b.y);
real[] rs = rtpalette(c, H, pa, pb);
isomodulus(z, a, b, rs);
isophase(z, a, b);
draw(box(a, b));
f(z)=arctanz=2i1log1−iz1+iz
import domcol;
size(15cm);
pair f(pair z) { z = (0, 1) * z; return 1 / (0, 0.5) * log((1 + z) / (1 - z)); }
pair a = (-3, -3), b = (3, 3);
real c = 0;
pair[][] z = map_rect(f, a, b);
int[] H = image(z, a, b, c, reverse=true);
xaxis(Bottom, a.x, b.x, RightTicks(N=2, n=5));
yaxis(Left, a.y, b.y, LeftTicks(N=2, n=5));
pair pa = (b.x + 0.25, a.y);
pair pb = (b.x + 1.25, b.y);
real[] rs = rtpalette(c, H, pa, pb);
isomodulus(z, a, b, rs);
isophase(z, a, b);
draw(box(a, b));
f(z)=arctanhz=21log1−z1+z
import domcol;
size(15cm);
pair f(pair z) { return 0.5 * log((1 + z) / (1 - z)); }
pair a = (-3, -3), b = (3, 3);
real c = 0;
pair[][] z = map_rect(f, a, b);
int[] H = image(z, a, b, c, reverse=true);
xaxis(Bottom, a.x, b.x, RightTicks(N=2, n=5));
yaxis(Left, a.y, b.y, LeftTicks(N=2, n=5));
pair pa = (b.x + 0.25, a.y);
pair pb = (b.x + 1.25, b.y);
real[] rs = rtpalette(c, H, pa, pb);
isomodulus(z, a, b, rs);
isophase(z, a, b);
draw(box(a, b));
f(z)=zα=eαlogz
f(z)=z2
import domcol;
size(15cm);
pair f(pair z) { return z * z; }
pair a = (-3, -3), b = (3, 3);
real c = 0;
pair[][] z = map_rect(f, a, b);
int[] H = image(z, a, b, c, reverse=true);
xaxis(Bottom, a.x, b.x, RightTicks(N=2, n=3));
yaxis(Left, a.y, b.y, LeftTicks(N=2, n=3));
pair pa = (b.x + 0.25, a.y);
pair pb = (b.x + 1.25, b.y);
real[] rs = rtpalette(c, H, pa, pb);
isomodulus(z, a, b, rs);
isophase(z, a, b);
draw(box(a, b));
f(z)=z1/2=z
import domcol;
size(15cm);
pair f(pair z) { return sqrt(z); }
pair a = (-3, -3), b = (3, 3);
real c = 0;
pair[][] z = map_rect(f, a, b);
int[] H = image(z, a, b, c, reverse=true);
xaxis(Bottom, a.x, b.x, RightTicks(N=2, n=3));
yaxis(Left, a.y, b.y, LeftTicks(N=2, n=3));
pair pa = (b.x + 0.25, a.y);
pair pb = (b.x + 1.25, b.y);
real[] rs = rtpalette(c, H, pa, pb);
isomodulus(z, a, b, rs);
isophase(z, a, b);
draw(box(a, b));
f(z)=zi
import domcol;
size(15cm);
pair f(pair z) { return z**(0,1); }
pair a = (-3, -3), b = (3, 3);
real c = 0;
pair[][] z = map_rect(f, a, b);
int[] H = image(z, a, b, c, reverse=true);
xaxis(Bottom, a.x, b.x, RightTicks(N=2, n=3));
yaxis(Left, a.y, b.y, LeftTicks(N=2, n=3));
pair pa = (b.x + 0.25, a.y);
pair pb = (b.x + 1.25, b.y);
real[] rs = rtpalette(c, H, pa, pb);
isomodulus(z, a, b, rs);
isophase(z, a, b);
draw(box(a, b));
f(z)=z2+i
import domcol;
size(15cm);
pair f(pair z) { return z^(2, 1); }
pair a = (-3, -3), b = (3, 3);
real c = 0;
pair[][] z = map_rect(f, a, b);
int[] H = image(z, a, b, c, reverse=true);
xaxis(Bottom, a.x, b.x, RightTicks(N=2, n=3));
yaxis(Left, a.y, b.y, LeftTicks(N=2, n=3));
pair pa = (b.x + 0.25, a.y);
pair pb = (b.x + 1.25, b.y);
real[] rs = rtpalette(c, H, pa, pb);
isomodulus(z, a, b, rs);
isophase(z, a, b);
draw(box(a, b));
f(z)=Γ(z)
import domcol;
size(15cm);
pair f(pair z) { return gamma(z); }
pair a = (-5, -5), b = (5, 5);
real c = 0;
pair[][] z = map_rect(f, a, b);
int[] H = image(z, a, b, c, reverse=true);
xaxis(Bottom, a.x, b.x, RightTicks(N=2, n=5));
yaxis(Left, a.y, b.y, LeftTicks(N=2, n=5));
pair pa = (b.x + 0.5, a.y);
pair pb = (b.x + 2, b.y);
real[] rs = rtpalette(c, H, pa, pb);
isomodulus(z, a, b, rs);
isophase(z, a, b);
draw(box(a, b));
f(z)=(iz)−1−1(iz)−8−(iz)−1
import domcol;
size(15cm);
pen pal(real l, real t) { return palHSY(l, t, a=0.8, b=0.4); }
pair f(pair z) { z *= (0, 1); return (z**(-8) - 1 / z) / (1 / z - 1); }
pair a = (-2, -2), b = (2, 2);
real c = 0;
pair[][] z = map_rect(f, a, b, 500, 500);
int[] H = image(f, a, b, c, pal);
xaxis(YEquals(a.y), xmin=a.x, xmax=b.x, RightTicks(N=2, n=2));
yaxis(XEquals(a.x), ymin=a.y, ymax=b.y, LeftTicks(N=2, n=2));
pair pa = (b.x + 0.2, a.y);
pair pb = (b.x + 0.7, b.y);
rtpalette(c, H, pa, pb, pal);
isophase(z, a, b);
draw(box(a, b));